Finite Group DatabasebetaFinite Group Databasebeta| order | 22308 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C13 |
| direct product | C11×C3⋊#10621729 |
| unambiguous semidirect product | C3⋊(C11×#10621729) |
| Fitting, socle, Hall | C3×C11×C132 ⋊ C4 |
| derived, Hall | C3×C132 ⋊ C4×C11 |
| Hall | C11×C132 ⋊ Dic3 |
| Sylow | C132 ⋊ C11×Dic3 |
| Hall | C3×C11 ⋊ #10621729 |
| Sylow | C3 ⋊ C11×#10621729 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C3⋊#10621729 |
| commutator, hypocenter | C3×C132 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C132 | C4 |
| prime radical | C3×C11×C13⋊D13 | C2 |
| cosocle | C3×C13⋊D13 | C2×C11 |
| LCS | G ▷ C3×C132 | |
| UCS | C1 ◁ C11 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 858 |
1452 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22308, 165);